A conic trust-region method for optimization with nonlinear equality and inequality constrains via active-set strategy (Q864760)

The following nonlinear optimization problem is considered: \[ \min f_0(x)\text{ subject to }f_i(x)= 0,\quad\forall i\in E,\;f_j(x)\leq 0\;\forall j\in I, \] where \(E\), \(I\) are given finite index sets and \(f_k\) are twice continuously differentiable functions for all \(k\in E\cup I\cup\{0\}\). A new algorithm for solving this optimization problem is proposed. The algorithm combines conic model methods, trust region techniques and active-set strategies. Further a new approximate method for the trust region sub-problem is suggested. Global convergence of the proposed algorithm is obtained. In the concluding part of the paper, the algorithm is demonstrated on small numerical examples.